On recent developments in the theory of boundary value problems for impulsive fractional differential equations

Authors:
Jinrong Wang;Yong Zhou;Michal Feckan
Affiliations:
Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, PR China;Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia and Mathematic ...
Venue:
Computers & Mathematics with Applications
Year:
2012

Citing 6
Cited 1

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions

Computers & Mathematics with Applications
Existence results for the three-point impulsive boundary value problem involving fractional differential equations

Computers & Mathematics with Applications
Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions

Computers & Mathematics with Applications
Impulsive boundary value problem for nonlinear differential equations of fractional order

Computers & Mathematics with Applications
Some new existence results for fractional differential inclusions with boundary conditions

Mathematical and Computer Modelling: An International Journal

Existence of solutions for fractional impulsive neutral functional differential equations with infinite delay

Neurocomputing

Quantified Score

Hi-index	0.09

Visualization

Abstract

This paper is motivated from some recent papers treating the boundary value problems for impulsive fractional differential equations. We first make a counterexample to show that the formula of solutions in cited papers are incorrect. Second, we establish a general framework to find the solutions for impulsive fractional boundary value problems, which will provide an effective way to deal with such problems. Third, some sufficient conditions for the existence of the solutions are established by applying fixed point methods. Meanwhile, data dependence is obtained by using a new generalized singular Gronwall inequality. Finally, three examples are given to illustrate the results.